Nuprl Lemma : bag-deq-member_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[b:bag(A)]. ∀[x:A]. (bag-deq-member(eq;x;b) ∈ 𝔹)
Proof
Definitions occuring in Statement :
bag-deq-member: bag-deq-member(eq;x;b),
bag: bag(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
bag: bag(T),
member: t ∈ T,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bag-deq-member: bag-deq-member(eq;x;b),
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T},
prop: ℙ
Lemmas referenced :
bool_wf,
list_wf,
iff_imp_equal_bool,
deq-member_wf,
assert-deq-member,
member-permutation,
assert_wf,
permutation_wf,
equal_wf,
equal-wf-base,
bag_wf,
deq_wf
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
pointwiseFunctionalityForEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
equalitySymmetry,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaFormation,
because_Cache,
rename,
independent_isectElimination,
independent_pairFormation,
dependent_functionElimination,
independent_functionElimination,
productEquality,
universeEquality,
isect_memberFormation,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[b:bag(A)]. \mforall{}[x:A]. (bag-deq-member(eq;x;b) \mmember{} \mBbbB{})
Date html generated:
2018_05_21-PM-09_47_14
Last ObjectModification:
2017_07_26-PM-06_30_08
Theory : bags_2
Home
Index